By building on the approach introduced by McGuirl et al. [1]} (see §REF ), we use dimension-1 topological features, which correspond to loops or holes in our data, to count stripes and interstripes, define stripe and interstripe width, and flag broken or incomplete stripes and interstripes.
Using the cropped, cleaned data from Step 2, we calculate pairwise distances between \(M\)  cells, between \(X^\text{d}\)  cells, and between \(X^\ell \)  cells on a domain that is periodic in \(x\) . (Because we crop the CA patterns so that our CA and ABM domains have the same length in Step 1, we note that specifying boundary conditions that are periodic in \(x\)  on these cropped domains is an approximation for CA patterns.) We compute persistent homology in dimension 0 and dimension 1 based on these pairwise distances using Ripser [2]}, enforcing a maximum distance of 650 \(\mu \) m in our filtration.
